Archimedes
,
Archimedis De iis qvae vehvntvr in aqva libri dvo
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ARCHIMEDIS
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<
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">Ex quibus perſpicuum eſt lineas omnes ſic ductas ab
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ipſis ſectionibus in eandem proportionem ſecari. </
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<
s
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diuidendo, conuertendoque cm ad mb, & </
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ce ad ea.</
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<
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">LEMMA III.</
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">Sed & </
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<
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">illud constare potest; </
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<
s
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">lineas, quæ in portioni-
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bus eiuſmodi ſimilibus ita ducuntur, ut cú baſibus æqua-
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les angulos contineant, ab ipſis ſimiles quoque portiones
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abſcindere: </
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<
s
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">hoc eſt, ut in propoſita figura, portiones h b c,
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m f c, quas lineæ c h, c m abſcindunt, etiam inter ſe
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ſimiles eſſe.</
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<
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>
enim ch, cm bifariam in punctis p q: </
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xml:space
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">& </
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">per
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ipſa ducantur lineæ r p s, t q u diametris æquidiſtantes. </
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<
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xml:space
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">erit portio-
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nis b s c diameter p s, & </
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xml:space
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">portionis m u c diameter q u. </
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<
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">Itaque fiat
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ut quadratum c r ad quadratum c p, ita linea b n ad aliam lineam,
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quæ ſit s x: </
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xml:space
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">& </
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">ut quadratum c t ad quadratum c q, ita fiat f o ad
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u y. </
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">iam exijs
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47
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quæ demóſtra
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uimus in com-
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mentarijs in
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quartam pro-
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poſitioné. </
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chrmedis de co
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noidibus, & </
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ſphæroidibus,
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patet quadra-
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tum c p æqua-
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le eſſe rectan-
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gulo p s x:</
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